I have no idea what to do...How do you solve h(t)=400-16t^2?

Question

please show steps

Answer 1

This is a difference of squares factoring problem. 400 is the square of 20 and 16t^2 is the square of 4t.
To solve, you set the equation = 0. Then factor as:
(20 + 4t) * (20 - 4t) = 0.
Set each factor equal to zero, and solve for t.

good luck!

Answer 2

Well, what do you mean by "solve"? What you've given is an expression for a function, but it doesn't really ask for a solution.

If you are asked to find the roots of the function, i.e. the values of t for which h(t) is zero (in other words, where it touches or crosses the x-axis), then here's how I would approach it:

You want to know when the function has a value of zero:
h(t) = 400 - 16t^2 = 0

These things are always easier when you get the variable (t) on one side of the equation and everything else on the other side. First you want to get rid of the 400 on the left side of the equation. (The reason you want to do that first is that 400 is a separate term from the variable [t], not something being multiplied by t. You want to get rid of separate terms first.)

If you subtract 400 from both sides, you get
400 - 400 - 16t^2 = 0 - 400
Since 400 - 400 = 0, this equation simplifies to
- 16t^2 = -400

Now that you've gotten rid of the term that doesn't include t, you want to get rid of the -16 that's being multiplied by t^2, You want to divide by -16 to get rid of it. Divide both sides of the equation by -16, and you get
-16t^2 / -16 = -400 / -16
which simplifies to
t^2 = 25

Since you've got the variable (t) being squared, now you want to take the square root of both sides. Remember that square roots usually give you two answers:
t = 5 or t = -5

So the roots of the function h(t) = 400 - 16t^2
are t = 5 and t = -5.

Answer 3

You can't solve THAT - it's not an equation, it's a definition. It defines a function of t. It happens to describe the height of an object released from a point 400 feet above the ground.

Now if someone asked you to find t when the height above ground [ h(t) ] is zero, for example, THEN you'd have an equation:

0=400-16t^2.

Solving that should be easy - subtract 400 from both sides, divide by -16, etc.

Answer 4

h(t) = 400 - 16t^2

What about it? I'm going to take a wild guess and assume you want to solve h(t) = 0.

0 = 400 - 16t^2

16t^2 = 400

Divide both sides by 16,

t^2 = 25

Take the square root of both sides. Remember that by the square root property, we have to include "plus or minus" to our answer in addition to taking the square root.

t = +/- 5

Therefore, our solutions for t are
t = {5, -5}

Answer 5

Well, to 'solve' a function, you have to find where h(t) = 0. To do that, you substitute 0 in for h(t). From there, you solve. I prefer to factor, since you can here, to get

0 = (20 + 4t) (20 - 4t)
Set each of the factors to zero and solve for t. I got +/-5. If t is referring to time, then you have to throw out the -5, so all you have left is 5.

Answer 6

well, 16t^2 = 4t*4t and 400 = 20*20
so 400-16t^2 = (20+4t)*(20-4t) = h(t)
when h(t) = 0, 20-4t = 0 so t = 5
t cannot be -5 because t has to be >=0

Answer 7

h(t)=400-16t^2
(a+b)(a-b)=a^2-b^2
=(-4t +?)
=(4t +?)
Please note that 20 *20 is 400 so we choose it
0 = (4t+20)(20-4t)
0= 4t+ 20
-5 = t ******
or
20-4t = 0
20 = 4t
5 = t *****
***** is the answer line
and we choose 0 because we want to find the value of t.

If you need help,visit my website which should be finished soon. www.edexter93.wetpaint.com

Answer 8

(20-4t)(20+4t)

400-80t-80t-16t^2

-80t and 80t =0

400-16t^2 is left over.

Answer 9

You don't - there's nothing to solve.
Instead of math you should learn how to properly phrase questions.